| // Copyright 2022 The Go Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| //go:build ignore |
| // +build ignore |
| |
| // This program is run via "go generate" (via a directive in sort.go) |
| // to generate implementation variants of the underlying sorting algorithm. |
| // When passed the -generic flag it generates generic variants of sorting; |
| // otherwise it generates the non-generic variants used by the sort package. |
| |
| package main |
| |
| import ( |
| "bytes" |
| "flag" |
| "fmt" |
| "go/format" |
| "log" |
| "os" |
| "text/template" |
| ) |
| |
| type Variant struct { |
| // Name is the variant name: should be unique among variants. |
| Name string |
| |
| // Path is the file path into which the generator will emit the code for this |
| // variant. |
| Path string |
| |
| // Package is the package this code will be emitted into. |
| Package string |
| |
| // Imports is the imports needed for this package. |
| Imports string |
| |
| // FuncSuffix is appended to all function names in this variant's code. All |
| // suffixes should be unique within a package. |
| FuncSuffix string |
| |
| // DataType is the type of the data parameter of functions in this variant's |
| // code. |
| DataType string |
| |
| // TypeParam is the optional type parameter for the function. |
| TypeParam string |
| |
| // ExtraParam is an extra parameter to pass to the function. Should begin with |
| // ", " to separate from other params. |
| ExtraParam string |
| |
| // ExtraArg is an extra argument to pass to calls between functions; typically |
| // it invokes ExtraParam. Should begin with ", " to separate from other args. |
| ExtraArg string |
| |
| // Funcs is a map of functions used from within the template. The following |
| // functions are expected to exist: |
| // |
| // Less (name, i, j): |
| // emits a comparison expression that checks if the value `name` at |
| // index `i` is smaller than at index `j`. |
| // |
| // Swap (name, i, j): |
| // emits a statement that performs a data swap between elements `i` and |
| // `j` of the value `name`. |
| Funcs template.FuncMap |
| } |
| |
| func main() { |
| genGeneric := flag.Bool("generic", false, "generate generic versions") |
| flag.Parse() |
| |
| if *genGeneric { |
| generate(&Variant{ |
| Name: "generic_ordered", |
| Path: "zsortordered.go", |
| Package: "slices", |
| Imports: "import \"cmp\"\n", |
| FuncSuffix: "Ordered", |
| TypeParam: "[E cmp.Ordered]", |
| ExtraParam: "", |
| ExtraArg: "", |
| DataType: "[]E", |
| Funcs: template.FuncMap{ |
| "Less": func(name, i, j string) string { |
| return fmt.Sprintf("cmp.Less(%s[%s], %s[%s])", name, i, name, j) |
| }, |
| "Swap": func(name, i, j string) string { |
| return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i) |
| }, |
| }, |
| }) |
| |
| generate(&Variant{ |
| Name: "generic_func", |
| Path: "zsortanyfunc.go", |
| Package: "slices", |
| FuncSuffix: "CmpFunc", |
| TypeParam: "[E any]", |
| ExtraParam: ", cmp func(a, b E) int", |
| ExtraArg: ", cmp", |
| DataType: "[]E", |
| Funcs: template.FuncMap{ |
| "Less": func(name, i, j string) string { |
| return fmt.Sprintf("(cmp(%s[%s], %s[%s]) < 0)", name, i, name, j) |
| }, |
| "Swap": func(name, i, j string) string { |
| return fmt.Sprintf("%s[%s], %s[%s] = %s[%s], %s[%s]", name, i, name, j, name, j, name, i) |
| }, |
| }, |
| }) |
| } else { |
| generate(&Variant{ |
| Name: "interface", |
| Path: "zsortinterface.go", |
| Package: "sort", |
| Imports: "", |
| FuncSuffix: "", |
| TypeParam: "", |
| ExtraParam: "", |
| ExtraArg: "", |
| DataType: "Interface", |
| Funcs: template.FuncMap{ |
| "Less": func(name, i, j string) string { |
| return fmt.Sprintf("%s.Less(%s, %s)", name, i, j) |
| }, |
| "Swap": func(name, i, j string) string { |
| return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j) |
| }, |
| }, |
| }) |
| |
| generate(&Variant{ |
| Name: "func", |
| Path: "zsortfunc.go", |
| Package: "sort", |
| Imports: "", |
| FuncSuffix: "_func", |
| TypeParam: "", |
| ExtraParam: "", |
| ExtraArg: "", |
| DataType: "lessSwap", |
| Funcs: template.FuncMap{ |
| "Less": func(name, i, j string) string { |
| return fmt.Sprintf("%s.Less(%s, %s)", name, i, j) |
| }, |
| "Swap": func(name, i, j string) string { |
| return fmt.Sprintf("%s.Swap(%s, %s)", name, i, j) |
| }, |
| }, |
| }) |
| } |
| } |
| |
| // generate generates the code for variant `v` into a file named by `v.Path`. |
| func generate(v *Variant) { |
| // Parse templateCode anew for each variant because Parse requires Funcs to be |
| // registered, and it helps type-check the funcs. |
| tmpl, err := template.New("gen").Funcs(v.Funcs).Parse(templateCode) |
| if err != nil { |
| log.Fatal("template Parse:", err) |
| } |
| |
| var out bytes.Buffer |
| err = tmpl.Execute(&out, v) |
| if err != nil { |
| log.Fatal("template Execute:", err) |
| } |
| |
| formatted, err := format.Source(out.Bytes()) |
| if err != nil { |
| log.Fatal("format:", err) |
| } |
| |
| if err := os.WriteFile(v.Path, formatted, 0644); err != nil { |
| log.Fatal("WriteFile:", err) |
| } |
| } |
| |
| var templateCode = `// Code generated by gen_sort_variants.go; DO NOT EDIT. |
| |
| // Copyright 2022 The Go Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| package {{.Package}} |
| |
| {{.Imports}} |
| |
| // insertionSort{{.FuncSuffix}} sorts data[a:b] using insertion sort. |
| func insertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) { |
| for i := a + 1; i < b; i++ { |
| for j := i; j > a && {{Less "data" "j" "j-1"}}; j-- { |
| {{Swap "data" "j" "j-1"}} |
| } |
| } |
| } |
| |
| // siftDown{{.FuncSuffix}} implements the heap property on data[lo:hi]. |
| // first is an offset into the array where the root of the heap lies. |
| func siftDown{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, lo, hi, first int {{.ExtraParam}}) { |
| root := lo |
| for { |
| child := 2*root + 1 |
| if child >= hi { |
| break |
| } |
| if child+1 < hi && {{Less "data" "first+child" "first+child+1"}} { |
| child++ |
| } |
| if !{{Less "data" "first+root" "first+child"}} { |
| return |
| } |
| {{Swap "data" "first+root" "first+child"}} |
| root = child |
| } |
| } |
| |
| func heapSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) { |
| first := a |
| lo := 0 |
| hi := b - a |
| |
| // Build heap with greatest element at top. |
| for i := (hi - 1) / 2; i >= 0; i-- { |
| siftDown{{.FuncSuffix}}(data, i, hi, first {{.ExtraArg}}) |
| } |
| |
| // Pop elements, largest first, into end of data. |
| for i := hi - 1; i >= 0; i-- { |
| {{Swap "data" "first" "first+i"}} |
| siftDown{{.FuncSuffix}}(data, lo, i, first {{.ExtraArg}}) |
| } |
| } |
| |
| // pdqsort{{.FuncSuffix}} sorts data[a:b]. |
| // The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort. |
| // pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf |
| // C++ implementation: https://github.com/orlp/pdqsort |
| // Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/ |
| // limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort. |
| func pdqsort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, limit int {{.ExtraParam}}) { |
| const maxInsertion = 12 |
| |
| var ( |
| wasBalanced = true // whether the last partitioning was reasonably balanced |
| wasPartitioned = true // whether the slice was already partitioned |
| ) |
| |
| for { |
| length := b - a |
| |
| if length <= maxInsertion { |
| insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| return |
| } |
| |
| // Fall back to heapsort if too many bad choices were made. |
| if limit == 0 { |
| heapSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| return |
| } |
| |
| // If the last partitioning was imbalanced, we need to breaking patterns. |
| if !wasBalanced { |
| breakPatterns{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| limit-- |
| } |
| |
| pivot, hint := choosePivot{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| if hint == decreasingHint { |
| reverseRange{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| // The chosen pivot was pivot-a elements after the start of the array. |
| // After reversing it is pivot-a elements before the end of the array. |
| // The idea came from Rust's implementation. |
| pivot = (b - 1) - (pivot - a) |
| hint = increasingHint |
| } |
| |
| // The slice is likely already sorted. |
| if wasBalanced && wasPartitioned && hint == increasingHint { |
| if partialInsertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) { |
| return |
| } |
| } |
| |
| // Probably the slice contains many duplicate elements, partition the slice into |
| // elements equal to and elements greater than the pivot. |
| if a > 0 && !{{Less "data" "a-1" "pivot"}} { |
| mid := partitionEqual{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}}) |
| a = mid |
| continue |
| } |
| |
| mid, alreadyPartitioned := partition{{.FuncSuffix}}(data, a, b, pivot {{.ExtraArg}}) |
| wasPartitioned = alreadyPartitioned |
| |
| leftLen, rightLen := mid-a, b-mid |
| balanceThreshold := length / 8 |
| if leftLen < rightLen { |
| wasBalanced = leftLen >= balanceThreshold |
| pdqsort{{.FuncSuffix}}(data, a, mid, limit {{.ExtraArg}}) |
| a = mid + 1 |
| } else { |
| wasBalanced = rightLen >= balanceThreshold |
| pdqsort{{.FuncSuffix}}(data, mid+1, b, limit {{.ExtraArg}}) |
| b = mid |
| } |
| } |
| } |
| |
| // partition{{.FuncSuffix}} does one quicksort partition. |
| // Let p = data[pivot] |
| // Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot. |
| // On return, data[newpivot] = p |
| func partition{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int, alreadyPartitioned bool) { |
| {{Swap "data" "a" "pivot"}} |
| i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned |
| |
| for i <= j && {{Less "data" "i" "a"}} { |
| i++ |
| } |
| for i <= j && !{{Less "data" "j" "a"}} { |
| j-- |
| } |
| if i > j { |
| {{Swap "data" "j" "a"}} |
| return j, true |
| } |
| {{Swap "data" "i" "j"}} |
| i++ |
| j-- |
| |
| for { |
| for i <= j && {{Less "data" "i" "a"}} { |
| i++ |
| } |
| for i <= j && !{{Less "data" "j" "a"}} { |
| j-- |
| } |
| if i > j { |
| break |
| } |
| {{Swap "data" "i" "j"}} |
| i++ |
| j-- |
| } |
| {{Swap "data" "j" "a"}} |
| return j, false |
| } |
| |
| // partitionEqual{{.FuncSuffix}} partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot]. |
| // It assumed that data[a:b] does not contain elements smaller than the data[pivot]. |
| func partitionEqual{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, pivot int {{.ExtraParam}}) (newpivot int) { |
| {{Swap "data" "a" "pivot"}} |
| i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned |
| |
| for { |
| for i <= j && !{{Less "data" "a" "i"}} { |
| i++ |
| } |
| for i <= j && {{Less "data" "a" "j"}} { |
| j-- |
| } |
| if i > j { |
| break |
| } |
| {{Swap "data" "i" "j"}} |
| i++ |
| j-- |
| } |
| return i |
| } |
| |
| // partialInsertionSort{{.FuncSuffix}} partially sorts a slice, returns true if the slice is sorted at the end. |
| func partialInsertionSort{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) bool { |
| const ( |
| maxSteps = 5 // maximum number of adjacent out-of-order pairs that will get shifted |
| shortestShifting = 50 // don't shift any elements on short arrays |
| ) |
| i := a + 1 |
| for j := 0; j < maxSteps; j++ { |
| for i < b && !{{Less "data" "i" "i-1"}} { |
| i++ |
| } |
| |
| if i == b { |
| return true |
| } |
| |
| if b-a < shortestShifting { |
| return false |
| } |
| |
| {{Swap "data" "i" "i-1"}} |
| |
| // Shift the smaller one to the left. |
| if i-a >= 2 { |
| for j := i - 1; j >= 1; j-- { |
| if !{{Less "data" "j" "j-1"}} { |
| break |
| } |
| {{Swap "data" "j" "j-1"}} |
| } |
| } |
| // Shift the greater one to the right. |
| if b-i >= 2 { |
| for j := i + 1; j < b; j++ { |
| if !{{Less "data" "j" "j-1"}} { |
| break |
| } |
| {{Swap "data" "j" "j-1"}} |
| } |
| } |
| } |
| return false |
| } |
| |
| // breakPatterns{{.FuncSuffix}} scatters some elements around in an attempt to break some patterns |
| // that might cause imbalanced partitions in quicksort. |
| func breakPatterns{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) { |
| length := b - a |
| if length >= 8 { |
| random := xorshift(length) |
| modulus := nextPowerOfTwo(length) |
| |
| for idx := a + (length/4)*2 - 1; idx <= a + (length/4)*2 + 1; idx++ { |
| other := int(uint(random.Next()) & (modulus - 1)) |
| if other >= length { |
| other -= length |
| } |
| {{Swap "data" "idx" "a+other"}} |
| } |
| } |
| } |
| |
| // choosePivot{{.FuncSuffix}} chooses a pivot in data[a:b]. |
| // |
| // [0,8): chooses a static pivot. |
| // [8,shortestNinther): uses the simple median-of-three method. |
| // [shortestNinther,∞): uses the Tukey ninther method. |
| func choosePivot{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) (pivot int, hint sortedHint) { |
| const ( |
| shortestNinther = 50 |
| maxSwaps = 4 * 3 |
| ) |
| |
| l := b - a |
| |
| var ( |
| swaps int |
| i = a + l/4*1 |
| j = a + l/4*2 |
| k = a + l/4*3 |
| ) |
| |
| if l >= 8 { |
| if l >= shortestNinther { |
| // Tukey ninther method, the idea came from Rust's implementation. |
| i = medianAdjacent{{.FuncSuffix}}(data, i, &swaps {{.ExtraArg}}) |
| j = medianAdjacent{{.FuncSuffix}}(data, j, &swaps {{.ExtraArg}}) |
| k = medianAdjacent{{.FuncSuffix}}(data, k, &swaps {{.ExtraArg}}) |
| } |
| // Find the median among i, j, k and stores it into j. |
| j = median{{.FuncSuffix}}(data, i, j, k, &swaps {{.ExtraArg}}) |
| } |
| |
| switch swaps { |
| case 0: |
| return j, increasingHint |
| case maxSwaps: |
| return j, decreasingHint |
| default: |
| return j, unknownHint |
| } |
| } |
| |
| // order2{{.FuncSuffix}} returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a. |
| func order2{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int, swaps *int {{.ExtraParam}}) (int, int) { |
| if {{Less "data" "b" "a"}} { |
| *swaps++ |
| return b, a |
| } |
| return a, b |
| } |
| |
| // median{{.FuncSuffix}} returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c. |
| func median{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, c int, swaps *int {{.ExtraParam}}) int { |
| a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}}) |
| b, c = order2{{.FuncSuffix}}(data, b, c, swaps {{.ExtraArg}}) |
| a, b = order2{{.FuncSuffix}}(data, a, b, swaps {{.ExtraArg}}) |
| return b |
| } |
| |
| // medianAdjacent{{.FuncSuffix}} finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a. |
| func medianAdjacent{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a int, swaps *int {{.ExtraParam}}) int { |
| return median{{.FuncSuffix}}(data, a-1, a, a+1, swaps {{.ExtraArg}}) |
| } |
| |
| func reverseRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b int {{.ExtraParam}}) { |
| i := a |
| j := b - 1 |
| for i < j { |
| {{Swap "data" "i" "j"}} |
| i++ |
| j-- |
| } |
| } |
| |
| func swapRange{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, b, n int {{.ExtraParam}}) { |
| for i := 0; i < n; i++ { |
| {{Swap "data" "a+i" "b+i"}} |
| } |
| } |
| |
| func stable{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, n int {{.ExtraParam}}) { |
| blockSize := 20 // must be > 0 |
| a, b := 0, blockSize |
| for b <= n { |
| insertionSort{{.FuncSuffix}}(data, a, b {{.ExtraArg}}) |
| a = b |
| b += blockSize |
| } |
| insertionSort{{.FuncSuffix}}(data, a, n {{.ExtraArg}}) |
| |
| for blockSize < n { |
| a, b = 0, 2*blockSize |
| for b <= n { |
| symMerge{{.FuncSuffix}}(data, a, a+blockSize, b {{.ExtraArg}}) |
| a = b |
| b += 2 * blockSize |
| } |
| if m := a + blockSize; m < n { |
| symMerge{{.FuncSuffix}}(data, a, m, n {{.ExtraArg}}) |
| } |
| blockSize *= 2 |
| } |
| } |
| |
| // symMerge{{.FuncSuffix}} merges the two sorted subsequences data[a:m] and data[m:b] using |
| // the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum |
| // Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz |
| // Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in |
| // Computer Science, pages 714-723. Springer, 2004. |
| // |
| // Let M = m-a and N = b-n. Wolog M < N. |
| // The recursion depth is bound by ceil(log(N+M)). |
| // The algorithm needs O(M*log(N/M + 1)) calls to data.Less. |
| // The algorithm needs O((M+N)*log(M)) calls to data.Swap. |
| // |
| // The paper gives O((M+N)*log(M)) as the number of assignments assuming a |
| // rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation |
| // in the paper carries through for Swap operations, especially as the block |
| // swapping rotate uses only O(M+N) Swaps. |
| // |
| // symMerge assumes non-degenerate arguments: a < m && m < b. |
| // Having the caller check this condition eliminates many leaf recursion calls, |
| // which improves performance. |
| func symMerge{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) { |
| // Avoid unnecessary recursions of symMerge |
| // by direct insertion of data[a] into data[m:b] |
| // if data[a:m] only contains one element. |
| if m-a == 1 { |
| // Use binary search to find the lowest index i |
| // such that data[i] >= data[a] for m <= i < b. |
| // Exit the search loop with i == b in case no such index exists. |
| i := m |
| j := b |
| for i < j { |
| h := int(uint(i+j) >> 1) |
| if {{Less "data" "h" "a"}} { |
| i = h + 1 |
| } else { |
| j = h |
| } |
| } |
| // Swap values until data[a] reaches the position before i. |
| for k := a; k < i-1; k++ { |
| {{Swap "data" "k" "k+1"}} |
| } |
| return |
| } |
| |
| // Avoid unnecessary recursions of symMerge |
| // by direct insertion of data[m] into data[a:m] |
| // if data[m:b] only contains one element. |
| if b-m == 1 { |
| // Use binary search to find the lowest index i |
| // such that data[i] > data[m] for a <= i < m. |
| // Exit the search loop with i == m in case no such index exists. |
| i := a |
| j := m |
| for i < j { |
| h := int(uint(i+j) >> 1) |
| if !{{Less "data" "m" "h"}} { |
| i = h + 1 |
| } else { |
| j = h |
| } |
| } |
| // Swap values until data[m] reaches the position i. |
| for k := m; k > i; k-- { |
| {{Swap "data" "k" "k-1"}} |
| } |
| return |
| } |
| |
| mid := int(uint(a+b) >> 1) |
| n := mid + m |
| var start, r int |
| if m > mid { |
| start = n - b |
| r = mid |
| } else { |
| start = a |
| r = m |
| } |
| p := n - 1 |
| |
| for start < r { |
| c := int(uint(start+r) >> 1) |
| if !{{Less "data" "p-c" "c"}} { |
| start = c + 1 |
| } else { |
| r = c |
| } |
| } |
| |
| end := n - start |
| if start < m && m < end { |
| rotate{{.FuncSuffix}}(data, start, m, end {{.ExtraArg}}) |
| } |
| if a < start && start < mid { |
| symMerge{{.FuncSuffix}}(data, a, start, mid {{.ExtraArg}}) |
| } |
| if mid < end && end < b { |
| symMerge{{.FuncSuffix}}(data, mid, end, b {{.ExtraArg}}) |
| } |
| } |
| |
| // rotate{{.FuncSuffix}} rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data: |
| // Data of the form 'x u v y' is changed to 'x v u y'. |
| // rotate performs at most b-a many calls to data.Swap, |
| // and it assumes non-degenerate arguments: a < m && m < b. |
| func rotate{{.FuncSuffix}}{{.TypeParam}}(data {{.DataType}}, a, m, b int {{.ExtraParam}}) { |
| i := m - a |
| j := b - m |
| |
| for i != j { |
| if i > j { |
| swapRange{{.FuncSuffix}}(data, m-i, m, j {{.ExtraArg}}) |
| i -= j |
| } else { |
| swapRange{{.FuncSuffix}}(data, m-i, m+j-i, i {{.ExtraArg}}) |
| j -= i |
| } |
| } |
| // i == j |
| swapRange{{.FuncSuffix}}(data, m-i, m, i {{.ExtraArg}}) |
| } |
| ` |